Find the Exact Value tan(-(3pi)/4)

Problem

tan(−(3*π)/4)

Solution

1. Apply the odd function property of the tangent function, which states that tan(−θ)=−tan(θ)

tan(−(3*π)/4)=−tan((3*π)/4)

2. Identify the reference angle for (3*π)/4 Since the angle is in the second quadrant, the reference angle is π−(3*π)/4=π/4

Reference Angle=π/4

3. Determine the sign of the tangent function in the second quadrant. In Quadrant II, tangent is negative.

tan((3*π)/4)=−tan(π/4)

4. Substitute the known value for tan(π/4) which is 1

tan((3*π)/4)=−1

5. Combine the results by substituting back into the expression from step 1.

−tan((3*π)/4)=−(−1)

6. Simplify the final expression.

−(−1)=1

Final Answer

tan(−(3*π)/4)=1

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